An algorithm for counting short cycles in bipartite graphs

Halford, Thomas R.; Chugg, K.M.

doi:10.1109/tit.2005.860472

Cited by 80 publications

(84 citation statements)

References 17 publications

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“…In order to compute I 6 , we apply the method proposed by Halford and Chugg in [26]. Let us define the following matrix notations:…”

Section: B Number Of Cycles Of Length 6 Andmentioning

confidence: 99%

“…The results provided by (12) and (13) have been successfully cross-checked with the software library developed by Halford and Chugg [26]. It used to be downloadable, but this is unfortunately no longer the case.…”

Section: Let Us Also Definementioning

confidence: 99%

“…As for the computation of I 6 , we apply the method proposed in [26] for the evaluation of I 8 the number of cycles of length 8. The girth of the decoding graph is g = 6.…”

Section: B Computation Of Imentioning

confidence: 99%

“…where ,6) and L U (5,2) are matrices defined in [26], and A = EE T . The trace of these matrices can be computed, as it has been done in the Appendix A for I 6 : …”

Section: B Computation Of Imentioning

confidence: 99%

“…The first step of the algorithm requires to count the number of cycles of length 6 and 8. To do so, we implemented the method proposed by Halford and Chugg in [26] to derive analytical formulas. Then, lower bounds on the number of cycles of length 6 and 8 are determined.…”

Section: Introductionmentioning

confidence: 99%

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Selection of Parity Check Equations For the Iterative Message-Passing Detection of M-Sequences

Noes

Savin

Ros

et al. 2017

IEEE Trans. Commun.

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Abstract-We consider the joint detection and decoding of msequences. The receiver has to decide whether an m-sequence is received and possibly to decode its initial state. To do so, it implements an iterative message-passing decoding algorithm that operates on a parity check matrix, built upon a number of reference parity-check equations satisfied by the m-sequence. This matrix concatenates several elementary parity check matrices which are derived from reference equations. Unlike the conventional decoding case, the detection problem imposes to consider false alarms that may occur when the decoder is only fed with noise. While absorbing sets are known to be responsible for the error floor phenomenon of iterative message-passing decoders, we show that they may have a beneficial effect on the detection performance, in that they may prevent the decoder to produce false alarms. We further compute the number of hybrid cycles of length 6 and 8 in the Tanner graph of the decoder and use the minimization of this number as criterion to derive an algorithm for selecting the reference parity check equations. This algorithm was found to be efficient for minimizing the probability of false alarm and decreases also the probability of wrong detection in the very small SNR region. This has been achieved at the cost of a reduction of the probability of correct detection.

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“…In order to compute I 6 , we apply the method proposed by Halford and Chugg in [26]. Let us define the following matrix notations:…”

Section: B Number Of Cycles Of Length 6 Andmentioning

confidence: 99%

Section: Let Us Also Definementioning

confidence: 99%

“…As for the computation of I 6 , we apply the method proposed in [26] for the evaluation of I 8 the number of cycles of length 8. The girth of the decoding graph is g = 6.…”

Section: B Computation Of Imentioning

confidence: 99%

“…where ,6) and L U (5,2) are matrices defined in [26], and A = EE T . The trace of these matrices can be computed, as it has been done in the Appendix A for I 6 : …”

Section: B Computation Of Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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